To make a side cast tilt the casting plane of the overhead cast
over to the side. Tilt the rod all the way over to the horizontal.
It's a great way
of throwing narrow forward loops, but it's
most useful for casting in tight spots. Five
benefits appear:

we don't have to take
the rod up to the vertical where it's
going to clunk on branches

our back loop can be
kept low and parallel to the water
and can be send underneath
overhanging foliage behind us

the loop on the
forward cast is horizontal, which is
really useful for sending under
branches

and we can keep this
forward loop really low to the water

side casting helps
keep the rod outside the fishes
window of vision.

Side casting is also useful
for casting into the teeth of a gale - for
two reasons: one is that taking the rod high
into the air allows it to get blown around
and the other is that if our leader doesn't
straighten out properly on the forward cast,
it will simply land in a curve as opposed to
a heap.

Side casting can be performed
off both sides of the body, in order to cast
of the left hand side for right-handers (or
vice-versa) the recommended style is to
rotate the wrist so that the palm of the hand
is facing downwards.

Incidentally returning to
that 40yrds of the wrong shoulder cast,
doing this (i.e. putting the thumb behind the rod on the forward cast) makes this cast more
acceptable to some instructors - aren't we a
funny bunch?

A neat trick is the change of
direction side cast. The way to achieve this
is to perform the side cast as you normally
would and then on the last forward cast just
as the rod points in the direction you want
to cast, rotate the wrist so that the reel
points downwards. Many good stream anglers I
know use this to good effect: they do a
couple of false side casts to judge the right
distance, and whack! change of direction,
under the tree, dead on target.

Make sure that you point downwards with the rod tip on the final delivery, otherwise the line clashes with the rod...